Matter part of generalised entropy, REF , which is the entanglement entropy of the Hawking radiation in the presence of island surface can be calculated from the following formula[1]}, [2]}
\(S_{\rm matter}^{\rm BEH}({\cal R}\cup {\cal I}) = \frac{Q}{3} \log \left(\frac{d(a_1^+,a_1^-)d(b_1^+,b_1^-)d(a_1^+,b_1^+)d(a_1^-,b_1^-)}{d(a_1^+,b_1^-)d(a_1^-,b_1^+)}\right),\) 
